Chaotic behavior of countable products of homeomorphism groups
Dynamical Systems
2022-11-08 v2 Geometric Topology
Abstract
Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We construct numerous new examples of chaotic groups of homeomorphisms of countable products of various metrizable topological spaces, including infinite-dimensional topological manifolds, whose factors can be as noncompact surfaces, so triangulable closed manifolds of an arbitrary dimension.
Keywords
Cite
@article{arxiv.2206.10992,
title = {Chaotic behavior of countable products of homeomorphism groups},
author = {N. I. Zhukova and A. G. Korotkov},
journal= {arXiv preprint arXiv:2206.10992},
year = {2022}
}
Comments
31 pages, 8 figures